Analytic bootstrap of mixed correlators in the $\boldsymbol{O(n)}$ CFT

TL;DR

This paper applies advanced conformal bootstrap techniques to compute corrections to mixed correlators in the $O(n)$ Wilson-Fisher CFT near four dimensions, providing new data on scaling dimensions and OPE coefficients.

Contribution

It introduces a systematic method to calculate order-$oldsymbol{ extit{varepsilon}}$ corrections for mixed correlators in the $O(n)$ CFT, extending to higher orders and specific cases like the Ising model.

Findings

Computed order-$oldsymbol{ extit{varepsilon}}$ corrections to scaling dimensions and OPE coefficients.

Extended some calculations to order-$oldsymbol{ extit{varepsilon}}^2$ for the Ising case.

Discussed technical aspects like subleading corrections and multiplet recombination.

Abstract

We use large spin perturbation theory and the Lorentzian inversion formula to compute order-$\varepsilon$ corrections to mixed correlators in the $O(n)$ Wilson-Fisher CFT in $4 - \varepsilon$ dimensions. In particular, we find the scaling dimensions and averaged OPE coefficients appearing in all correlators involving $\varphi$ and $\varphi^2$, for $\varphi^2$ in both the singlet and symmetric traceless representations of $O(n)$. We extend some computations to the next order, and find order-$\varepsilon^2$ data for a number of quantities for the Ising case at $n = 1$. Along the way, we discuss several interesting technical aspects which arise, including subleading corrections to mixed conformal blocks, projections onto higher twists in the inversion formula, and multiplet recombination.